(b) Put the above linear programming problem in canonical form and solve it using the
Simplex algorithm.
[ 12 marks]
Q(6)
(a)State the fundamental theorem of linear programming. Show how this theorem
gives rise to the direct “sledgehammer” method for solving linear programming
models and explain why this direct “sledgehammer” method is not used to solve large
practical linear programming models.
[ 5 marks]
(b)Consider the linear programming model

1
P and
2
P respectively. One unit of
1
P occupies
1
M for
12
1
hours and
2
M for
30
1
hours
respectively. The corresponding figures for one unit of
2
P are for
1
M
60
1
hours
and
for
2
M
15
1
hours respectively. The net profit per unit of
1
P produced is € 50 and
for
per unit of
2
P produced is € 30(independent of whether the machines are used to
full

capacity or not). What production plan gives the most profit? Formulate this linear

programming problem and solve it graphically.
Hint: Let ·
1
x number of units of
1
P produced per hour and let ·
2
x number of
units
of
2
P produced per hour.
[ 9 marks]

¸
¸
·
H R
a
B
π
where R and H are respectively, the effective radius and height of the core and the
constant
a
has the approximate value of 2.40. Use the method of Lagrange
multipliers to show that the smallest volume for a specified fixed buckling is given
approximately by
3
148
B
and find the corresponding values of H and R .
[ 11 marks]
Answers to 2009 Exam
Q(1) Answer
(a)
2
2 2